this section will show you that all definitions can be interpreted "forwards" and "backwards" and can be either true or false. Statements like this are usually given in if and only-if form as biconditional statements, or as a conditional statement given in only-if and if-then forms where the hypothesis is followed by the conclusion. A conditional statement can be written as a converse statement which is the reverse of the conditional statement, and is written where the conclusion is the hypothesis and the hypothesis becomes the conclusion.
vocabulary: perpendicular lines- lines that intersect to form a right angle line perpendicular to a plane- a line that intersects a plane at a right angle and is perpendicular to every line in the plane biconditional statement- a statement written as a conditional and converse using the phrase if and only if (iff); it is also the same as writing a conditional statement and its converse.
examples:
1. based on the diagram is AC perpendicular to DB?
solution: Yes, because the right angle symbol in the diagram shows that line AC intersects line DB to for a right angle, so the lines are perpendicular.
2. conditional statements are not always written in if-then form, and are sometimes written in only-if form.
It is Thursday, only ifI have swim practice. ↑ Hypothesis ↑ Conclusion
statement rewritten in if-then form: If it is Thursday, thenI have swim practice.
statement written as a converse (or reverse): If i have swim practice, then it is Thursday.
statement written as a biconditional statement: It is Thursday, if and only ifi have swim practice.
3. conditional: If B lies between points G and E, thenGB+EB=GE
converse: IfGB+EB=GE, then B lies between points G and E
combining these two statements results in a true biconditional statemet.
biconditional: Point B lies between points G and E if and only if GB+EB=GE
practice problems:
1. Is line L2 perpendicular to line L1?
2. write the conditional statement as a biconditional statement.
If it is raining, then I need an umbrella.
3. Write the following conditional statement as its converse and biconditional.
If i am eating cookies, then I want a glass of milk.
4. Write and conditional and converse statement for the following biconditional statement.
A points on a line is collinear if and only if they are on the same line.
vocabulary:
perpendicular lines- lines that intersect to form a right angle
line perpendicular to a plane- a line that intersects a plane at a right angle and is perpendicular to every line in the plane
biconditional statement- a statement written as a conditional and converse using the phrase if and only if (iff); it is also the same as writing a conditional statement and its converse.
examples:
1. based on the diagram is AC perpendicular to DB?
solution: Yes, because the right angle symbol in the diagram shows that line AC intersects line DB to for a right angle, so the lines are perpendicular.
2. conditional statements are not always written in if-then form, and are sometimes written in only-if form.
It is Thursday, only if I have swim practice.
↑ Hypothesis ↑ Conclusion
statement rewritten in if-then form: If it is Thursday, then I have swim practice.
statement written as a converse (or reverse): If i have swim practice, then it is Thursday.
statement written as a biconditional statement: It is Thursday, if and only if i have swim practice.
3. conditional: If B lies between points G and E, then GB+EB=GE
converse: If GB+EB=GE, then B lies between points G and E
combining these two statements results in a true biconditional statemet.
biconditional: Point B lies between points G and E if and only if GB+EB=GE
practice problems:
1. Is line L2 perpendicular to line L1?
2. write the conditional statement as a biconditional statement.
If it is raining, then I need an umbrella.
3. Write the following conditional statement as its converse and biconditional.
If i am eating cookies, then I want a glass of milk.
4. Write and conditional and converse statement for the following biconditional statement.
A points on a line is collinear if and only if they are on the same line.
web pages for extra help:
biconditional
logic- biconditional statements
pages in textbook: 79-87